Question

The second's hand of a watch has length $6cm$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

• A. $2\pi mm/s,0mm/s$
• B. $2\sqrt{2}\pi mm/s,4.44mm/s$
• C. $2\sqrt{2}\pi mm/s,2\pi mm/s$
• D. $2\pi mm/s,2\sqrt{2}\pi mm/s$

Answer 1

The correct option is D $2\pi mm/s,2\sqrt{2}\pi mm/s$

$v=\frac{2\pi r}{T}$
$v=\frac{2\pi 0.06}{60}$=$2\pi mm/s$

$|v_2-v_1|=\sqrt{(2\pi {)}^2+(2\pi {)}^2}=2\sqrt{2}\pi mm/s$